Question

Find the square root of 1296.

Answer 1

Hint: Use the steps of the square root by long division method to find the square root of a given problem.

Complete step-by-step answer:

In the question we have to find the square root of the number 1296.
First, we write the steps of doing Long division method for finding square roots:
Step 1: First group the digits in pairs, starting with the digit in units place. Each pair and the remaining digit (if any) is called a period.
Step 2: Think of the largest number whose square is equal to or just less than the first period. Taking this number as a divisor and also the quotient.
Step 3: Subtract the product of the divisor and the quotient from the first period and bring down the next period to the right of the remainder. This makes a new dividend.
Step 4: Now, the new divisor is obtained by taking two times the quotient and annexing the suitable digit which is also taken as the next digit of quotient, chosen in such a way that the product of the new divisor and the digits is equal or just less than the new dividend.
Step 5: Repeat steps (2), (3), (4) till all the periods have been taken up. Now, the quotient so obtained is the required square root of the given number.
Let’s take an example of finding square root of 784,
\[\begin{align}
  & 2\left| \text{ }784 \right.\text{ }\left( 28 \right. \\
 & \text{ }\underline{-4\text{ }} \\
 & 48\left| \text{ }384 \right. \\
 & \text{ }\underline{-384} \\
 & \text{ 0} \\
\end{align}\]
Here, the square root is 28.
Now, let’s take the number 1296.
\[\begin{align}
  & \text{ 3}\left| \text{ }\overline{12} \right.\text{ }\overline{96}\text{ }\left( 36 \right. \\
 & \text{ }\underline{-9\text{ }} \\
 & 66\left| \text{ }396 \right. \\
 & \text{ }\underline{-396} \\
 & \text{ 000} \\
\end{align}\]
So, the square root of number 1296 is 36.
The answer is 36.

Note: There is also another method to find square root by prime factorization method. Let’s do it as an example for let’s say the number be 36. So at first, we will factorize into prime factors like this,

So, we can write 36 as $2\times 2\times 3\times 3$
Now, to find a square root we will replace every two same factors by a single factor, so the square root of 36 will be $2\times 3$ or 6.